What I usually do is keep the previous OS in another partititon and copy only the files I need from one partition to the other.
I also left the old operating system as backup in case something goes wrong.
Since you already have a separate / and /home partition, you can proceed to use the installer and select Something else... to point to the existing partitions.
If you use the same username - use the live session to delete the dot files from the home partition before you reboot to your new install. CTRL+H will reveal them. They'll be re-created when you next login.
If you use a different username - the old home folder remains intact, in which you can move the folders to the new user after the new installation is finished.
This is assuming, of course, this isn't an encrypted home folder.
For guidance, @wolfman has written a guide on this type of installation: